On the same day, Trump's National Security Adviser John Bolton called the New York Times article "utter nonsense".
A full withdrawal of USA troops was unlikely, the officials said, according to the paper.
President Moon Jae-in's approval rating has shot up to an 11-month high this week, a poll showed Thursday, following his historic summit with North Korean leader Kim Jong-un that raised hopes for denuclearization of the communist state.
Trump said that his team remained in "constant contact" with North Korean officials to try to secure the release of detained Americans. "As I said yesterday, stay tuned", Trump added.
In the declaration, Moon and Kim also pledged to sign a multilateral agreement to formally end the Korean War.
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Amid easing tensions between the USA and North Korea, those within Trump's orbit have hinted that the hostages would soon be released.
"The President has not asked the Pentagon to provide options for reducing American forces stationed in South Korea", Bolton said in a written statement.
The United States has been demanding the North free Kim Hak-song, Kim Sang-duk and Kim Dong-chul and reports have said the two sides were close to reaching a deal on their release. "North Korea watches us as much as we follow North Korea".
Jung Pak, a former Central Intelligence Agency analyst, said the danger for the United States in Trump's public flirtations with removing troops is that he is giving up leverage to Kim in advance of the summit.
Speaking about the summit, Mr Trump said: "We now have a date and we have a location".
Earlier this week, the U.S. president suggested that the demilitarised zone, or DMZ, between North and South Korea would be an excellent venue for the planned summit, but that Singapore was also a possible site.